NDLI: On expansions in orthogonal polynomials

Content Provider	Springer Nature Link
Author	Iserles, Arieh Cantero, María José
Copyright Year	2011
Abstract	A recently introduced fast algorithm for the computation of the first N terms in an expansion of an analytic function into ultraspherical polynomials consists of three steps: Firstly, each expansion coefficient is represented as a linear combination of derivatives; secondly, it is represented, using the Cauchy integral formula, as a contour integral of the function multiplied by a kernel; finally, the integrand is transformed to accelerate the convergence of the Taylor expansion of the kernel, allowing for rapid computation using Fast Fourier Transform. In the current paper we demonstrate that the first two steps remain valid in the general setting of orthogonal polynomials on the real line with finite support, orthogonal polynomials on the unit circle and Laurent orthogonal polynomials on the unit circle.
Ending Page	61
Page Count	27
Starting Page	35
File Format	PDF
ISSN	10197168
e-ISSN	15729044
Journal	Advances in Computational Mathematics
Issue Number	1
Volume Number	38
Language	English
Publisher	Springer US
Publisher Date	2011-10-21
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Hypergeometric functions Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Algebra Calculus of Variations and Optimal Control; Optimization Orthogonal functions and polynomials, general theory Orthogonal polynomials Numeric Computing Fast expansions Mathematics Theory of Computation Jacobi matrix Moment problems, interpolation problems
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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